Answer:
The equation in the point-slope form is y - 6 = [tex]\frac{2}{3}[/tex] (x - 3)
The equation in the slope-intercept form is y = [tex]\frac{2}{3}[/tex] x + 4
Step-by-step explanation:
The point-slope form of the linear equation is y - y1 = m(x - x1), where
- (x1, y1) is a point on the line
The slop-intercept form of the linear equation is y = m x + b, where
The slope of the equation in the form ax + by = c is m = [tex]\frac{-a}{b}[/tex], where
let us solve the question
∵ The line passes through the point (3, 6)
∴ x1 = 3 and y1 = 6
∵ The slope of the line equal the slope of the line 2x - 3y = 4
∴ a = 2 and b = -3
→ By using the third rule above
∴ m = [tex]\frac{-2}{-3}[/tex]
∴ m = [tex]\frac{2}{3}[/tex]
→ Substitute the values of m, x1, and x2 in the point-slope form above
∵ y - 6 = [tex]\frac{2}{3}[/tex] (x - 3)
∴ The equation in the point-slope form is y - 6 = [tex]\frac{2}{3}[/tex] (x - 3)
→ Substitute the value of m in the slope-intercept form above
∵ y = [tex]\frac{2}{3}[/tex] x + b
∵ The line passes through the point (3, 6)
→ Substitute x by 3 and y by 6 to find b
∵ 6 = [tex]\frac{2}{3}[/tex] (3) + b
∴ 6 = 2 + b
→ Subtract 2 from both sides
∴ 6 - 2 = 2 - 2 + b
∴ 4 = b
→ Substitute the value of b in the equation
∴ y = [tex]\frac{2}{3}[/tex] x + 4
∴ The equation in the slope-intercept form is y = [tex]\frac{2}{3}[/tex] x + 4
