Slope/Standard Form questions...?

Question

1. Find the x and y intercepts of the line given the equation: 7x+2y=-2
2. Write the equation 2y=12-5x in standard form.
3. What is the standard form of the equation y=1/4x-3?
4. Find the slope and y-intercept of the line: 5x-3y=19

Answer 1

1.
7x+2y=-21
write the equation in slope-intercept form y =mx + b. m = slope and b is y-intercept.
y = -7/2x -21/2
y-intercepts is -21/2.
x-intercept is where the line crosses the x-axis, so y = 0
x-intercept = -21/7=-3
2.
standard form line equation is Ax + By = C
2y=12-5x
add 5x to each side
5x+2y = 12
3.
standard form line equation is Ax + By = C
y=1/4x-3
multiply each side by 4
4y = x-12
standard form line equations is
x-4y = 12
4.
write the equation in slope-intercept form y =mx + b. m = slope and b is y-intercept.
5x-3y=19
y = 5/3x -19/3
slope = 5/3 and y-intercept = -19/3