GKT101: General Knowledge for Teachers – Math

1. $y=-\frac{3}{2} x+3$.

We are asked to complete the equation in slope-intercept form: $y=m \cdot x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

By looking at the graph, we can see that the $y$-intercept is $(0,3)$.

In order to find the slope, we need another point on the line whose coordinates are clearly visible. Such a point is $(2,0)$.

Now, to find the slope, we need to take the ratio of the corresponding differences in the $y$-values and the $x$-values:

$\frac{0-3}{2-0}=\frac{-3}{2}=-\frac{3}{2}$

The equation is $y=-\frac{3}{2} x+3$.

2. $y=2 x+4$.

We are asked to complete the equation in slope-intercept form: $y=m \cdot x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

By looking at the graph, we can see that the $y$-intercept is $(0,4)$.

In order to find the slope, we need another point on the line whose coordinates are clearly visible. Such a point is $(1,6)$.

Now, to find the slope, we need to take the ratio of the corresponding differences in the $y$-values and the $x$-values:

$\frac{6-4}{1-0}=\frac{2}{1}=2$

The equation is $y=2 x+4$.

3. $y=\frac{3}{4} x-2$.

We are asked to complete the equation in slope-intercept form: $y=m \cdot x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

By looking at the graph, we can see that the $y$-intercept is $(4,1)$.

Now, to find the slope, we need to take the ratio of the corresponding differences in the $y$-values and the $x$-values:

$\frac{1-(-2)}{4-0}=\frac{3}{4}$

The equation is $y=\frac{3}{4} x-2$.

4. $y=x-5$.

We are asked to complete the equation in slope-intercept form: $y=m \cdot x+b$. In this form, $m$ gives us the slope of the line and $b$ gives us its $y$-intercept.

By looking at the graph, we can see that the $y$-intercept is $(1,-4)$.

In order to find the slope, we need another point on the line whose coordinates are clearly visible. Such a point is $(1,-4)$.

Now, to find the slope, we need to take the ratio of the corresponding differences in the $y$-values and the $x$-values:

$\frac{-4-(-5)}{1-0}=\frac{1}{1}=1$

The equation is $y=x-5$.