Question

graph the line with slope $\frac{1}{2}$ passing through the point $(-5,2)$.

Explanation:

Step1: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m=\frac{1}{2}$, $x_1=-5$ and $y_1 = 2$. So, $y - 2=\frac{1}{2}(x + 5)$.

Step2: Convert to slope - intercept form

Expand the right - hand side: $y-2=\frac{1}{2}x+\frac{5}{2}$. Then add 2 to both sides: $y=\frac{1}{2}x+\frac{5}{2}+2=\frac{1}{2}x+\frac{5 + 4}{2}=\frac{1}{2}x+\frac{9}{2}$.

Step3: Find the y - intercept

In the slope - intercept form $y=mx + b$ ($m$ is slope and $b$ is y - intercept), for $y=\frac{1}{2}x+\frac{9}{2}$, the y - intercept is $\frac{9}{2}=4.5$. So the line crosses the y - axis at the point $(0,4.5)$.

Step4: Use the slope to find another point

The slope $m = \frac{1}{2}=\frac{\text{rise}}{\text{run}}$. Starting from the point $(0,4.5)$, if we move 2 units to the right (run = 2), we move 1 unit up (rise = 1). So another point is $(2,5.5)$.

Step5: Graph the line

Plot the points $(-5,2)$, $(0,4.5)$ and $(2,5.5)$ and draw a straight line passing through them.

Answer:

Graph the line by plotting the points $(-5,2)$, $(0,4.5)$ and $(2,5.5)$ and drawing a straight line through them.