A line has the equation 4x-3y=-9. find the equation if the line parallel to that has a y-intercept of -1

The equation of the line that parallel to a line has equation 4x - 3y = -9 and has y-intercept of -1 is y = [tex]\frac{4}{3}[/tex] x - 1Step-by-step explanation:Parallel lines haveSame slopesDifferent y-interceptsThe slope-intercept form of equation of a line is y = mx + b, where mis the slope of the line and b is the y-intercept∵ The equation of a line is 4 x - 3 y = - 9- To find the slope of the line put its equation in the form of y = mx + b∵ 4 x - 3 y = -9- Subtract 4 x from both sides∴ -3 y = -4 x - 9- Divide all the terms of the equation by -3∴ [tex]y=\frac{4}{3}x+3[/tex]∴ The slope of the line = [tex]\frac{4}{3}[/tex]∵ Parallel lines have same slopes∵ The slope of the given line is [tex]\frac{4}{3}[/tex]∴ The slope of the new line = [tex]\frac{4}{3}[/tex]∵ The form of the equation is y = m x + b∴ y = [tex]\frac{4}{3}[/tex] x + b∵ b is the y-intercept∵ The y-intercept of the new line is -1∴ b = -1∴ y = [tex]\frac{4}{3}[/tex] x - 1The equation of the line that parallel to a line has equation 4x - 3y = -9 and has y-intercept of -1 is y = [tex]\frac{4}{3}[/tex] x - 1Learn more:You can learn more about equations of parallel lines in brainly.com/question/8628615#LearnwithBrainly