# How to Graph an Equation in Point-Slope Form?

We can easily graph the line in point-slope form with the slope of the line and a point on the line. In this step-by-step guide, you will learn how to graph a line in point-slope form. ## A step-by-step guide to graph an equation in point-slope form

If only one point and the slope of the line are used to represent the equation of the line, its general form can be defined as $$y-y_1=m(x-x_1)$$. In this case, m is the slope of the line, and $$(y_1, x_1)$$ is a point on the line whose coordinates are known. This form of line representation is called slope point form. To easily draw an equation in the form of a point-slope, do the following steps:

• Check the equation carefully so that it is exactly the same as the point-slope form. If there is no subtraction operation on each side of the equation, you must rewrite the equation.
• Find a point on the line (for example $$(y_1, x_1)$$) and the slope of the line. Use the $$m=\frac{change\:in\:y}{change\:in\:x}=\frac{rise}{run}$$ formula to find the slope of the line.
• Find the point on the graph. According to the slope you obtained, find the second point. By connecting these two points, draw the graph of the point-slope form equation.

### Graphing an Equation in Point-Slope Form– Example 1:

Graph the following line: $$y-2=\frac{1}{2}(x+3)$$

Solution:

First, check the point-slope form equation. If one side of the equation doesn’t use the subtraction operation, you should rewrite it with the subtraction sign: $$y-2=\frac{1}{2}(x+3)$$$$→y-2=\frac{1}{2}(x-(-3))$$. Find a random point on the straight line and the slope of the line. You can use the point that is used in the formula: $$(y_1, x_1)→(-3, 2)$$.

The slope is $$\frac{1}{2}$$. Use the random point and the value of slope to graph the line: find the point $$(-3, 2)$$ on the coordinate plane. The slope is $$\frac{1}{2}$$. So, move up $$1$$ unit and right $$2$$  units to find the other point on the straight line: $$(-1, 3)$$. Connect these two points and graph the line.

## Exercises for Graphing an Equation in Point-Slope Form

### Graph the following line.

• $$\color{blue}{y+2=\frac{1}{4}(x-2)}$$

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