To solve this problem, we need to understand the slope-intercept form of a linear equation. The standard form is:
y = mx + b
In this equation:
-
m represents the
slope.
-
b represents the
y-intercept.
We simply need to look at each given equation and identify which number corresponds to the position of
m (the slope) and which number corresponds to the position of
b (the y-intercept).
Let's go through them one by one:
1.
Equation: $y = -6x + 3$
* The number in front of x is -6, so the Slope is
-6.
* The constant number at the end is 3, so the y-intercept is
3.
2.
Equation: $y = \frac{3}{2}x + 3$
* The number in front of x is $\frac{3}{2}$, so the Slope is
$\frac{3}{2}$.
* The constant number at the end is 3, so the y-intercept is
3.
3.
Equation: $y = 4x + 5$
* The number in front of x is 4, so the Slope is
4.
* The constant number at the end is 5, so the y-intercept is
5.
4.
Equation: $y = -2x + 20$
* The number in front of x is -2, so the Slope is
-2.
* The constant number at the end is 20, so the y-intercept is
20.
5.
Equation: $y = -\frac{2}{3}x - 2$
* The number in front of x is $-\frac{2}{3}$, so the Slope is
$-\frac{2}{3}$.
* The constant number at the end is -2, so the y-intercept is
-2.
6.
Equation: $y = x - 18$
* This can be written as $y = 1x - 18$. The number in front of x is 1 (implied), so the Slope is
1.
* The constant number at the end is -18, so the y-intercept is
-18.
7.
Equation: $y = \frac{5}{3}x - 2$
* The number in front of x is $\frac{5}{3}$, so the Slope is
$\frac{5}{3}$.
* The constant number at the end is -2, so the y-intercept is
-2.
8.
Equation: $y = \frac{4}{5}x - 1$
* The number in front of x is $\frac{4}{5}$, so the Slope is
$\frac{4}{5}$.
* The constant number at the end is -1, so the y-intercept is
-1.
9.
Equation: $y = -\frac{8}{3}x + 4$
* The number in front of x is $-\frac{8}{3}$, so the Slope is
$-\frac{8}{3}$.
* The constant number at the end is 4, so the y-intercept is
4.
10.
Equation: $y = -4x + \frac{1}{4}$
* The number in front of x is -4, so the Slope is
-4.
* The constant number at the end is $\frac{1}{4}$, so the y-intercept is
$\frac{1}{4}$.
Final Answer:
1. Slope: -6, y-intercept: 3
2. Slope: 3/2, y-intercept: 3
3. Slope: 4, y-intercept: 5
4. Slope: -2, y-intercept: 20
5. Slope: -2/3, y-intercept: -2
6. Slope: 1, y-intercept: -18
7. Slope: 5/3, y-intercept: -2
8. Slope: 4/5, y-intercept: -1
9. Slope: -8/3, y-intercept: 4
10. Slope: -4, y-intercept: 1/4
Parent Tip: Review the logic above to help your child master the concept of linear equations slope intercept form worksheet.
