Question

a line passes through the points (7, 4) and (0, 3). what is its equation in slope - intercept form? write your answer using integers, proper fractions, and improper fractions in simplest form. y =

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (7, 4) and (0, 3), we have $x_1 = 7$, $y_1 = 4$, $x_2 = 0$, $y_2 = 3$.
So, $m = \frac{3 - 4}{0 - 7} = \frac{-1}{-7} = \frac{1}{7}$.

Step2: Find the y-intercept (b)

The slope - intercept form is $y = mx + b$. We know that the line passes through the point (0, 3). When $x = 0$, $y = 3$. Substituting $x = 0$, $y = 3$ and $m=\frac{1}{7}$ into $y=mx + b$, we get $3=\frac{1}{7}(0)+b$. So, $b = 3$.

Step3: Write the equation

Substitute $m=\frac{1}{7}$ and $b = 3$ into the slope - intercept form $y=mx + b$. We get $y=\frac{1}{7}x+3$.

Answer:

$\frac{1}{7}x + 3$