1. **Problem statement:** Given the linear equation $y = 5x - 4$, we need to find: (a) The value of $x$ when $y=0$. (b) The value of $y$ when $x=0$. (c) The points where the equation crosses the $x$- and $y$-axes. (d) Graph the equation. 2. **Formula and rules:** The equation is in slope-intercept form $y = mx + b$, where $m=5$ is the slope and $b=-4$ is the $y$-intercept. 3. **Part (a): Find $x$ when $y=0$** Set $y=0$: $$0 = 5x - 4$$ Add 4 to both sides: $$4 = 5x$$ Divide both sides by 5: $$x = \frac{4}{5}$$ 4. **Part (b): Find $y$ when $x=0$** Substitute $x=0$ into the equation: $$y = 5(0) - 4 = -4$$ 5. **Part (c): Find intercepts** - $x$-intercept is where $y=0$, which we found as $x=\frac{4}{5}$, so the point is $\left(\frac{4}{5}, 0\right)$. - $y$-intercept is where $x=0$, which we found as $y=-4$, so the point is $(0, -4)$. 6. **Part (d): Graph the equation** Using the table: - For $x=-2$, $y=5(-2)-4 = -10 -4 = -14$ - For $x=-1$, $y=5(-1)-4 = -5 -4 = -9$ - For $x=0$, $y=-4$ - For $x=1$, $y=5(1)-4=5-4=1$ - For $x=2$, $y=5(2)-4=10-4=6$ Plot these points and draw a straight line through them. **Final answers:** (a) $x=\frac{4}{5}$ (b) $y=-4$ (c) $x$-intercept at $\left(\frac{4}{5}, 0\right)$, $y$-intercept at $(0, -4)$ (d) Graph is a straight line through points $(-2,-14)$, $(-1,-9)$, $(0,-4)$, $(1,1)$, $(2,6)$.