Question

1. is the point (-3, 10) a solution to the equation y + 4 = -2x (yes or no) circle the correct response.
2. what is the x intercept for the equation 4x + y = 3
3. what is the y intercept for the equation 4x + y = 3
4. find the slope of the line that passes through the points (2, 7) and (5, 6).

m= _________

1. find the slope of the line that passes through the points (-2, 1) and (4, -3).

m=_________

1. find the slope of the line given the equation y = 4x - 3.

m=_________

1. write an equation of the line in y = mx + b form given the slope = 3 and the y intercept = -3

Explanation:

Step1: Substitute (-3,10) into equation

Substitute $x=-3$, $y=10$ into $y+4=-2x$:
$10+4=-2\times(-3)$
$14=6$ (False)

Step2: Find x-intercept of $4x+y=3$

Set $y=0$:
$4x+0=3$
$x=\frac{3}{4}$

Step3: Find y-intercept of $4x+y=3$

Set $x=0$:
$4\times0+y=3$
$y=3$

Step4: Calculate slope for (2,7) & (5,6)

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$:
$m=\frac{6-7}{5-2}=\frac{-1}{3}=-\frac{1}{3}$

Step5: Calculate slope for (-2,1) & (4,-3)

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$:
$m=\frac{-3-1}{4-(-2)}=\frac{-4}{6}=-\frac{2}{3}$

Step6: Identify slope from $y=4x-3$

Slope-intercept form $y=mx+b$, so $m=4$

Step7: Write line equation with $m=3, b=-3$

Substitute into $y=mx+b$:
$y=3x-3$

Answer:

1. NO
2. $\frac{3}{4}$
3. $3$
4. $-\frac{1}{3}$
5. $-\frac{2}{3}$
6. $4$
7. $y=3x-3$