Writing Linear Equations (y=mx+b) - Pre Algebra

1. A table has $x$-values 0, 1, 2 and $y$-values 4, 7, 10. Write the equation in $y = mx + b$ form.

   $y = 3x + 4$. $y$ rises 3 for each 1 in $x$, and $y = 4$ when $x = 0$.

2. A tank holds 240 gallons and drains 12 gallons per hour. Write an equation for the gallons $y$ after $x$ hours.

   $y = -12x + 240$. The starting amount is $b$, and the drain rate is a negative slope.

3. A gym charges a 30 dollar fee plus 20 dollars per month. Write an equation for the total cost $y$ after $x$ months.

   $y = 20x + 30$.

4. Write the equation of the line through $(1, 4)$ and $(3, 10)$.

   $y = 3x + 1$. Slope $\frac{6}{2} = 3$, and $4 = 3(1) + b$ gives $b = 1$.

5. Write the equation of the line with slope 3 and $y$-intercept $-2$.

   $y = 3x - 2$.

6. A candle is 10 inches tall and burns 0.75 inch per hour. Write an equation for its height $y$ after $x$ hours.

   $y = -0.75x + 10$.

7. Write the equation of the horizontal line through $(3, -6)$.

   $y = -6$. A horizontal line has slope 0, so $y$ is constant.

8. Write the equation of the line with slope 2 through $(2, 7)$.

   $y = 2x + 3$. $7 = 2(2) + b$ gives $b = 3$.

9. Write the equation of the line through $(0, 5)$ and $(2, 11)$.

   $y = 3x + 5$. Slope $\frac{11 - 5}{2 - 0} = 3$, and $b = 5$.

10. Write the equation of the line through $(4, 10)$ and $(8, 18)$.

    $y = 2x + 2$. Slope $\frac{8}{4} = 2$, and $10 = 2(4) + b$ gives $b = 2$.

11. Rewrite $2x + y = 7$ in slope-intercept form.

    $y = -2x + 7$. Subtract $2x$ from both sides.

12. Write the equation of the line with slope $-\frac{1}{2}$ through $(0, 4)$.

    $y = -\frac{1}{2}x + 4$. The point $(0, 4)$ gives $b = 4$.

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