Question

write an equation in slope-intercept form of the line that passes through the points.
the image shows a coordinate grid with a line passing through the points (-1, 3) and (0, 4). there is also a box at the bottom with y = and a square to fill in the equation.

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept ($b$)

The y - intercept is the value of $y$ when $x = 0$. From the point $(0,4)$, we can see that when $x = 0$, $y=4$. So, $b = 4$.

Step3: Calculate the slope ($m$)

The formula for slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We have the points $(-1,3)$ and $(0,4)$. Let $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(0,4)$. Then $m=\frac{4 - 3}{0-(-1)}=\frac{1}{1}=1$.

Step4: Write the equation

Substitute $m = 1$ and $b = 4$ into the slope - intercept form $y=mx + b$. We get $y=1x + 4$ or $y=x + 4$.

Answer:

$y = x + 4$