Gradient and Y-Intercept in Linear Equations

The slope $(m)$ is the number in front of the variable $x$, called the coefficient. In this case, -4 is the coefficient of $x$, so the correct answer is -4.

The y-intercept is the value of $y$ when $x=0$. In the equation $y=5x-7$, when $x=0$, $y=-7$.

The slope $(m)$ is the coefficient of $x$. In this equation, the coefficient of $x$ is 1, so the slope is 1.

The equation of a straight line is written as $y=mx+c$, where $m$ is the slope and $c$ is the y-intercept. Here, $m=4$ and $c=-2$, so the equation is $y=4x-2$.

Doubling the slope means multiplying the original slope $(m=3)$ by 2, which gives a new slope of 6. The y-intercept $(c=-4)$ stays the same, so the new equation is $y=6x-4$.

The slope is the change in $y$ for each unit change in $x$. In this equation, the slope is 3, meaning for every increase of 1 in $x$, $y$ increases by 3.