Question

Line l passes through the point of intersection,A, of the lines 4x-3y+4=0 and x+2y=5. Without finding A,find the equation of line l if its y-intercept is 1.5

Answer 1

Answer:

$\large\boxed{y=\dfrac{15}{14}x+1.5}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

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You must solve the system of equations:

$\left\{\begin{array}{ccc}4x-3y+4=0&(1)\\x+2y=5&(2)\\y=mx+1.5&(3)\end{array}\right\qquad\text{substitute (3) to (1) and (2)}\\\\\left\{\begin{array}{ccc}4x-3(mx+1.5)+4=0\\x+2(mx+1.5)=5\end{array}\right\qquad\text{use the distributive property}\\\left\{\begin{array}{ccc}4x-3mx-4.5+4=0\\x+2mx+3=5&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx-0.5=0&\text{add 0.5 to both sides}\\x+2mx=2\end{array}\right\\\left\{\begin{array}{ccc}4x-3mx=0.5&\text{multiply both sides by 2}\\x+2mx=2&\text{multiply both sides by 3}\end{array}\righ$

$\underline{+\left\{\begin{array}{ccc}8x-6mx=1\\3x+6mx=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad11x=7\qquad\text{divide both sides by 11}\\.\qquad x=\dfrac{7}{11}\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\\dfrac{7}{11}+2m\left(\dfrac{7}{11}\right)=2\qquad\text{multiply both sides by 11}\\\\7+2m(7)=22\qquad\text{subtract 7 from both sides}\\\\14m=15\qquad\text{divide both sides by 14}\\\\m=\dfrac{15}{14}$