The equation of the straight line ${L_1}$ is $y = 2x - 3.$

Write down the $y$-intercept of ${L_1}$ .

Write down the gradient of ${L_1}$ .

The line ${L_2}$ is parallel to ${L_1}$ and passes through the point $(0,\,\,3)$ .

Write down the equation of ${L_2}$ .

The line ${L_3}$ is perpendicular to ${L_1}$ and passes through the point $( - 2,\,\,6).$

Write down the gradient of ${L_3}.$

Find the equation of ${L_3}$ . Give your answer in the form $ax + by + d = 0$ , where $a$ , $b$ and $d$ are integers.

$(0,\,\, - 3)$       (A1)     (C1)

Note: Accept $- 3$ or $y =  - 3.$

$2$       (A1)     (C1)

$y = 2x + 3$        (A1)(ft)     (C1)

Note: Award (A1)(ft) for correct equation. Follow through from part (b)
Award (A0) for ${L_2} = 2x + 3$.

$- \frac{1}{2}$             (A1)(ft)     (C1)

Note: Follow through from part (b).

$6 =  - \frac{1}{2}( - 2) + c$        (M1)

$c = 5$  (may be implied)

OR

$y - 6 =  - \frac{1}{2}(x + 2)$        (M1)

Note: Award (M1) for correct substitution of their gradient in part (d) and the point $( - 2,\,\,6)$. Follow through from part (d).

$x + 2y - 10 = 0$  (or any integer multiple)        (A1)(ft)     (C2)

Note: Follow through from (d). The answer must be in the form $ax + by + d = 0$ for the (A1)(ft) to be awarded. Accept any integer multiple.

Question 12: Linear function.

Many candidates demonstrated a good understanding of linear functions so successfully found the $y$-intercepts, gradient and equation in the form $y = mx + c$. However only the very best were able to rewrite this in the form $ax + by + d = 0$ where $a$, $b$ and $d$ are integers.

Question 12: Linear function.

Many candidates demonstrated a good understanding of linear functions so successfully found the $y$-intercepts, gradient and equation in the form $y = mx + c$. However only the very best were able to rewrite this in the form $ax + by + d = 0$ where $a$, $b$ and $d$ are integers.

Question 12: Linear function.

Many candidates demonstrated a good understanding of linear functions so successfully found the $y$-intercepts, gradient and equation in the form $y = mx + c$. However only the very best were able to rewrite this in the form $ax + by + d = 0$ where $a$, $b$ and $d$ are integers.

Question 12: Linear function.

Many candidates demonstrated a good understanding of linear functions so successfully found the $y$-intercepts, gradient and equation in the form $y = mx + c$. However only the very best were able to rewrite this in the form $ax + by + d = 0$ where $a$, $b$ and $d$ are integers.

Question 12: Linear function.

Many candidates demonstrated a good understanding of linear functions so successfully found the $y$-intercepts, gradient and equation in the form $y = mx + c$. However only the very best were able to rewrite this in the form $ax + by + d = 0$ where $a$, $b$ and $d$ are integers.