Finding the Equation of a Straight Line

Feedback: Not quite! 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.

Feedback: Not quite! 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.

Feedback: Not quite! 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.

Feedback: Not quite! The slope is calculated by the formula $\frac{\text{change in } y}{\text{change in } x}$. For these points, $\frac{7 - 3}{4 - 2} = 2$.

Feedback: Not quite! To find the equation, first calculate the slope (m) using the formula: $\frac{\text{change in } y}{\text{change in } x} = \frac{9 - 5}{2 - 0} = 2$. Since the line passes through (0, 5), the y-intercept (c) is 5. Thus, the equation is $y = 2x + 5$.

Feedback: Not quite! First, calculate the slope (m) using the formula $\frac{\text{change in } y}{\text{change in } x}: \frac{8 - 2}{3 - 1} = \frac{6}{2} = 3$. Next, use the point (1, 2) and the equation $y = mx + c$ to find the y-intercept (c): $c = 2 - 3(1) = 2 - 3 = -1$. So, the equation of the line is $y = 3x - 1$.