Question

write an equation of a line in slope-intercept form with the given slope and point. slope: 4, point: (3, 5)

Explanation:

Step1: Recall the point - slope formula

The point - slope form of a linear equation is \( y - y_1=m(x - x_1) \), where \( m \) is the slope and \( (x_1,y_1) \) is a point on the line. We know that \( m = 4 \), \( x_1=3 \) and \( y_1 = 5 \). Substitute these values into the point - slope formula:
\( y - 5=4(x - 3) \)

Step2: Expand the right - hand side

Using the distributive property \( a(b - c)=ab - ac \), where \( a = 4 \), \( b=x \) and \( c = 3 \), we get:
\( y - 5=4x-12 \)

Step3: Solve for y (slope - intercept form \( y=mx + b \))

Add 5 to both sides of the equation:
\( y=4x-12 + 5 \)
Simplify the right - hand side:
\( y=4x-7 \)

Answer:

\( y = 4x - 7 \)