Answer:
Required equations in standard form are:
1. 3x+4y=12
2. -5x+2y = 10
Step-by-step explanation:
Standard form of equation is given as:
[tex]Ax+By = C[/tex]
1. x – intercept is 4 and y – intercept is 3.
The points will be:
(4,0) and (0,3)
Slope: m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{3-0}{0-4}\\m = -\frac{3}{4}[/tex]
Slope intercept form of line is:
[tex]y = mx+b[/tex]
Putting the values of m and b(y-intercept)
[tex]y = -\frac{3}{4}x+3[/tex]
Multiplying whole equation by 4
[tex]4y = -3x+12\\3x+4y = 12[/tex]
2. x – intercept is -2 and y – intercept is 5
The points will be:
(-2,0) and (0,5)
Now
[tex]m = \frac{5-0}{0+2}\\m = \frac{5}{2}[/tex]
Putting the values of m and b in slope intercept form
[tex]y = \frac{5}{2}x+5[/tex]
Multiplying the equation by 2
[tex]2y = 5x+10[/tex]
[tex]-5x+2y=10[/tex]
Hence,
Required equations in standard form are:
1. 3x+4y=12
2. -5x+2y = 10
