Overview
A line’s slope tells how y changes with x, and its intercept gives y when x is zero. To build a line from a point and slope, impose that the point satisfy y = mx + b and solve for b. Standard form can be rearranged to show slope and intercept.
Consider this example: Which expression for y describes a line with slope 3 and y-intercept −4? The slope is the coefficient of x and the intercept is the constant. Therefore y = 3x − 4. Swapping the two numbers changes both properties.
The method also handles a different case: A line has slope −2 and passes through (3, 1). Which expression equals y on the line? Use y = −2x + b and substitute the point: 1 = −6 + b, so b = 7. Thus y = −2x + 7. The point’s y coordinate 1 is not the intercept because x is 3.
For a further application, consider: The line 3x − 2y = 8 is rewritten as y = mx + b. What expression is y? Subtract 3x to get −2y = 8 − 3x, then divide by −2: y = (3/2)x − 4. Both terms on the right change sign under division.
Using a point’s y coordinate as the intercept works only when its x coordinate is zero. Switching the signs while isolating y changes the line. After finding a new line equation, substitute every supplied point and compare its slope with the intended direction. Both checks are needed to establish the line.