Finding the Equation of a Straight Line

The y-intercept $(c)$ is the point where the line crosses the y-axis, i.e., when $x=0$. The slope $(m)$ represents how steep the line is.

The formula for the slope $(m)$ is the change in $y$ divided by the change in $x$. This gives us the steepness of the line.

When we substitute $x=-2$ into the equation $y=2x-1$, we get $y=-5$, which does not match the given y-coordinate of -4. Therefore, the point does not lie on the line.

The slope is calculated using the formula $\frac{\text{change in }y}{\text{change in }x}$. For these points, $\frac{7-3}{4-2}=2$.

First calculate the slope using $\frac{9-5}{2-0}=2$. Since the line passes through $(0,5)$, the y-intercept $(c)$ is 5. Thus, the equation is $y=2x+5$.

First, calculate the slope using $\frac{8-2}{3-1}=3$. Next, use the point $(1,2)$ and the equation $y=mx+c$ to find the y-intercept: $2=3(1)+c$, so $c=-1$. Therefore, the equation of the line is $y=3x-1$.