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## Applied Linear Equations 1 - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=1, Mode=m-pt

 1.   In slope-intercept form, write the equation of a line that goes through point (0, -5) with slope 1/4. Equation: 2.   In slope-intercept form, write the equation of a line that goes through point (-4, 2) with slope 2/3. Equation:

### Complexity=1, Mode=pt-pt

 1.   In slope-intercept form, write the equation of a line that goes through point (4, 4) and (-4, 0). Equation: 2.   In slope-intercept form, write the equation of a line that goes through point (1, 0) and (3, -4). Equation:

### Complexity=1, Mode=m-pt

1In slope-intercept form, write the equation of a line that goes through point (0, -5) with slope 1/4.
Equation:
Solution
Plug what you know into y=mx+b to get this:

Now solve for b:
b = - 5

Plug m and b back into y=mx+b to get the answer

Alternate Solution
Start by plugging the slope and point into point-slope form

Now solve for y

2In slope-intercept form, write the equation of a line that goes through point (-4, 2) with slope 2/3.
Equation:
Solution
Plug what you know into y=mx+b to get this:

Now solve for b:

Plug m and b back into y=mx+b to get the answer

Alternate Solution
Start by plugging the slope and point into point-slope form

Now solve for y

### Complexity=1, Mode=pt-pt

1In slope-intercept form, write the equation of a line that goes through point (4, 4) and (-4, 0).
Equation:
Solution
Calculate the slope:
(y2 - y1) / (x2 - x1) =
(0 - 4) / (-4 - 4) =
 12

Plug (4, 4) into y=mx+b to get this:

Now solve for b:
b = 2

Plug m and b back into y=mx+b to get the answer

Alternate Solution
Plug the slope and (4, 4) into point-slope form

Now solve for y

2In slope-intercept form, write the equation of a line that goes through point (1, 0) and (3, -4).
Equation:
Solution
Calculate the slope:
(y2 - y1) / (x2 - x1) =
(-4 - 0) / (3 - 1) =
-2

Plug (1, 0) into y=mx+b to get this:
0 = - 2 • 1 + b

Now solve for b:
b = 2

Plug m and b back into y=mx+b to get the answer
y = - 2x + 2

Alternate Solution
Plug the slope and (1, 0) into point-slope form
y = - 2(x - 1)

Now solve for y
y = - 2x + 2   