write and graph a linear equation in standard form and/or slope - intercept form.\n7) ( 5y = 3x )\n8) ( 3x…

7)

Step1: Convert to standard form (Ax + By = C)

Starting with (5y=3x), subtract (3x) from both sides: (- 3x+5y = 0) (standard form, where (A=-3), (B = 5), (C = 0))

Step2: Convert to slope - intercept form (y=mx + b)

Divide the original equation (5y = 3x) by (5): (y=\frac{3}{5}x+0) (slope - intercept form, where (m=\frac{3}{5}) and (b = 0))

Step3: Graph the equation

• For (y=\frac{3}{5}x), when (x = 0), (y=0) (the (y) - intercept is ((0,0)))
• When (x=5), (y = 3). Plot the points ((0,0)) and ((5,3)) and draw a straight line through them.

8)

Step1: Convert to slope - intercept form (y=mx + b)

Starting with (3x-y=14), subtract (3x) from both sides: (-y=-3x + 14). Multiply through by (- 1): (y = 3x-14) (slope - intercept form, where (m = 3) and (b=-14))

Step2: Convert to standard form (Ax+By = C)

The equation (3x-y=14) is already in standard form ((A = 3), (B=-1), (C = 14))

Step3: Graph the equation

• For (y = 3x-14), when (x = 0), (y=-14) (the (y) - intercept is ((0,-14)))
• When (y = 0), (3x-14=0), so (3x=14) and (x=\frac{14}{3}\approx4.67). Plot the points ((0,-14)) and ((\frac{14}{3},0)) and draw a straight line through them.

Answer:

7. Standard form: (-3x + 5y=0); Slope - intercept form: (y=\frac{3}{5}x)
8. Standard form: (3x-y=14); Slope - intercept form: (y = 3x-14)