Question

question 4
all work for this question must be shown on the cap #3
worksheet!

part a:
write the equation of the line that passes through the points (-1, 5)
and (4, 7). your answer should be in slope - intercept form.

• 5 points

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \((-1, 5)\) and \((4, 7)\), we have \( x_1=-1,y_1 = 5,x_2 = 4,y_2=7 \). So \( m=\frac{7 - 5}{4-(-1)}=\frac{2}{5} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((-1,5)\) and \( m = \frac{2}{5} \). Substituting these values, we get \( y - 5=\frac{2}{5}(x+ 1) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y - 5=\frac{2}{5}x+\frac{2}{5} \). Then add 5 to both sides. Since \( 5=\frac{25}{5} \), we have \( y=\frac{2}{5}x+\frac{2}{5}+\frac{25}{5}=\frac{2}{5}x+\frac{27}{5} \).

Answer:

The equation of the line in slope - intercept form is \( y=\frac{2}{5}x+\frac{27}{5} \)