Question

write an equation in slope - intercept form for the line described.
x - intercept (-3,0), y - intercept (0,5)
the equation of the line is y = \square
(simplify your answer. type your answer in slope - intercept form. use integers or fractions for any numbers 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. We know that the y - intercept $b$ is given by the point $(0,5)$, so $b = 5$.

Step2: Calculate the slope $m$

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. We have two points: the x - intercept $(-3,0)$ (so $x_1=-3,y_1 = 0$) and the y - intercept $(0,5)$ (so $x_2 = 0,y_2=5$).
Substitute these values into the slope formula: $m=\frac{5 - 0}{0-(-3)}=\frac{5}{3}$.

Step3: Write the equation

Now that we know $m=\frac{5}{3}$ and $b = 5$, substitute these values into the slope - intercept form $y=mx + b$.
We get $y=\frac{5}{3}x+5$.

Answer:

$\frac{5}{3}x + 5$