Q&A for How to Find the Equation of a Line

Using the equation, set x equal to zero and solve for y to find the y-intercept, or set y equal to zero and solve for x to find the x-intercept.

You multiply the whole equation by -1 to remove the negative sign. For example, if the question is: -y=-5x+1, you would then change the question to: -y*(-1) = (-5x+1)*(-1), and then get: y=5x-1.

Express the equation in standard form, y = mx + b, where m is the slope, and b is the y-intercept.

Yes, y = 3x - 5.

That means the line you're looking for would be defined as x = b: the line is vertical, m is "undefined" (infinity), and b is the x-intercept.

Take the x- and y-coordinates of the point, and insert them into the equation of the line. If the equation holds true with those x and y values inserted, the point is on the line.

Assuming a given straight line in the form of y = mx + b, any parallel line would have the same form with the same "m" but a different "b."

A "system" consists of at least two different equations (and thus at least two lines on a graph). As the above article explains, two pieces of information are required in order to define a line: a point and a slope. To "solve a system with only one given point," the point would have to be the intersection of the lines, and you would then need each line's slope.

As the above article explains, two pieces of information are required in order to define a straight line: the line's slope and a point on the line. If you don't know the slope, you could have an infinite number of lines passing through a given point.

All right-angled triangles have two vertices of 45 degrees and one of 90 degrees.

The slope (m) is -2. You're given values for x and y (5 and 4). Plug all those values into y = mx + b, and you'll find b. So 4 = -2(5) + b. Then 4 = -10 + b, and 14 = b. So the equation you're looking for is y = -2x + 14.

It's not possible. Assuming "one coordinate" means "one point" (and thus you know only one point through which the line passes), there could be an infinite number of lines passing through that one point.

A slope of -1 means that the line loses one unit on the y-axis for every unit it gains on the x-axis. Thus, as this line moves (gains) from -2 to zero on the x-axis, it moves (loses) from 4 to 2 on the y-axis. Thus, its y-intercept is 2. Using the standard form y = mx + b, m (the slope) is given as (-1), and b (the y-intercept) is found to be 2. The equation is therefore y = (-1)x + (2) = -x + 2 = 2 - x.

Any horizontal line will be represented by an equation in which y is equal to a constant (for example, y = 4). The constant will be the y-coordinate of the point through which the line passes. For example, if the horizontal line passes through the point (3,2), the equation will be y = 2.

See Find the Slope of a Line and related articles.

Use Method 2 above.

For each of the points A, B and C, plug the known coordinate into the equation and solve for the unknown coordinate. For example, for point A, y is 6, so solve for x: 6 = -2x + 3. Then 3 = -2x, and x = -3/2. So A is (-3/2, 6). Do the same for B (where x is already known) and C (where y is already known).

The line will have a slope of +3, because it's parallel to y = 3x - 4, and it will intercept the y-axis at +2, because it passes through (0,2). Therefore, the equation of the line is y = 3x + 2.

A straight line passing through (3,6) with a gradient of 2 will pass through the origin (0,0). That's because every point on the line is 2 units above the x-axis for every 1 unit it is to the right of the y-axis. (Thus, it passes through (3,6).) Therefore, the y-intercept is 0, and the equation of the line is y = 2x + 0 or y = 2x.

To find the slope, use the formula m = (y2 - y1) / (x2 - x1). So the slope is (6 - 3) / (-2 - 4) = 3 / -6 = -1/2. The slope-intercept formula is y = mx + b. So y = (-½)x + b. To find b, plug either of the x/y coordinates given in the question into this last slope-intercept equation. 3 = (-½)(4) + b. Then 3 = -2 + b, and 5 = b. So the equation of the line is y = (-½)x + 5. (If you don't like the look of that equation, you could express it as y = 5 - (x/2), or 2y = 10 - x.)

Any line parallel to a line ax + by + c = 0 is of the form ax + by + k = 0. Substitute the point given in the second equation to determine k.

In the case of the linear equation y = mx + b, b is the y-intercept. In other cases where y equals some expression in x, set x equal to 0, and y will be equal to the y-intercept.

A is twice as far from B as the midpoint is. On the x-axis, the midpoint is 6 - 4 = 2 units from B, so A is 4 units from B. That means that A's x-coordinate is 6 - 4 = 2. On the y-axis, the midpoint is 5 - 3 = 2 units from B, so A is also 4 units from B on that axis. That means that A's y-coordinate is 5 - 4 = 1. So the A coordinates are (2,1).

Assuming a compass is unavailable or not large enough, use a string, rope or chain. Set one end of it at a convenient point for the center, and set a pencil, chalk or stylus at a convenient radius along the string, etc. Draw the circle around the point.

Yes it can. For example the equation: y=-2x+3, where -2 is the slope and 3 is the y intercept. If you graph this, it forms a negative line.

You would take the slope from that line and use the above example to use the given point and the slope to figure out which point would be the slope the line would go through.

If you mean that you are given two points on the line, and the x-coordinates of the points are the same, while the y-coordinates are not the same, you're describing a vertical line (parallel to the y-axis). The equation of the line is x = a, where "a" is the x-coordinate of the two given points (and every other point on the line).

Only straight lines have a single slope. Straight lines, however, do not have tangents.

x=9 is a vertical line (parallel to the y-axis). So the equation you're looking for is of a line that's also vertical, meaning that the equation will take the form of x=a ("a" being the line's distance from the y-axis). Since this line passes through (-2,1), it's a vertical line two units to the left of the y-axis. Its equation is x = -2.

All points on the y-axis have an x value of 0. So 0 Is the x-coordinate. To find the y-coordinate, let x be zero in the equation y = x + 2. On this line when x is zero, y is 2. So the point you're looking for is (0,2).