Question

question what is an equation of the line that passes through the points (4, -7) and (8, -6)? answer attempt 1 out of 2 student answer

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 \( (4, -7) \) and \( (8, -6) \), we have \( x_1 = 4,y_1=-7,x_2 = 8,y_2=-6 \). So \( m=\frac{-6-(-7)}{8 - 4}=\frac{-6 + 7}{4}=\frac{1}{4} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \( (4,-7) \) and \( m=\frac{1}{4} \). Substituting these values, we get \( y-(-7)=\frac{1}{4}(x - 4) \).

Step3: Simplify the equation

Simplify \( y + 7=\frac{1}{4}x-1 \). Subtract 7 from both sides: \( y=\frac{1}{4}x-1 - 7 \), so \( y=\frac{1}{4}x-8 \). We can also write it in standard form: \( x-4y = 32 \) (by multiplying both sides by 4: \( 4y=x - 32 \), then \( x-4y=32 \)) or in other equivalent forms.

Answer:

One possible equation is \( y=\frac{1}{4}x - 8 \) (or \( x-4y = 32 \) or other equivalent linear equations)