Question

Find the equation of the line.

Answer 1

Answer:

y=1/2 +1.5

Step-by-step explanation:

y intercept = 1.5

gradient = rise over run = 1/2

y = 1/2 +1.5

Answer 2

Answer:

$y=\frac{1}{2}x+\frac{3}{2}$

Step-by-step explanation:

Slope-intercept form: $y=mx+b$ when $m$ is the slope and $b$ is the y-intercept (the y-coordinate of the point where the line crosses the y-axis)

1) Find the slope ($m$)

$m=\frac{y_2-y_1}{x_2-x_1}$ when the given points are $(x_1,y_1)$ and $(x_2,y_2)$

We can use any two points on the line to plug into this equation, but it's often easiest to use points that have whole-number coordinates. For example, we can use the points (1,-1) and (3,0).

$m=\frac{0-(-1)}{3-1}$

Two negatives make a positive

$m=\frac{0+1}{3-1}\\m=\frac{1}{2}$

So far, our equation looks like this:

$y=\frac{1}{2}x+b$

2) Find the y-intercept ($b$)

We're told to approximate the y-intercept based on what appears to be true in the graph. In the graph, we can see that the y-intercept appears to occur when y=-1.5, or when y=$-\frac{3}{2}$. Therefore, $b=\frac{-3}{2}$.

Now, after plugging both $m$ and $b$ into our equation, our final equation looks like this:

$y=\frac{1}{2}x+\frac{3}{2}$

I hope this helps!