(a) Find the gradient of the line $$ A B $$. (b) On the graph, draw the line with equation $$ y=2 x $$. (c) Write down the coordinates of the point where the two lines intersect.

Question

UpStudy AI · Accepted Answer

Let the points be  
$$
A(2,3) \quad \text{and} \quad B(6,7).
$$

**(a) Finding the gradient of the line $$AB$$:**

The gradient $$m$$ of a line joining two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is given by  
$$
m=\frac{y_2-y_1}{x_2-x_1}.
$$
Substitute the coordinates of $$A$$ and $$B$$:
$$
m=\frac{7-3}{6-2}=\frac{4}{4}=1.
$$

---

**(b) Drawing the line with equation $$y=2x$$:**

The equation  
$$
y=2x
$$
represents a straight line with a gradient of 2 and a $$y$$-intercept of 0. When plotting:

- When $$x=0$$, $$y=0$$ (so the line passes through the origin).
- When $$x=1$$, $$y=2$$.
- When $$x=2$$, $$y=4$$.

Plot these points and draw a straight line through them.

---

**(c) Finding the coordinates of the intersection of the two lines:**

The line $$AB$$ passes through $$A(2,3)$$ and $$B(6,7)$$ so its equation can be found using the point–gradient form. Since the gradient of $$AB$$ is 1, use point $$A$$ to obtain
$$
y-3=1(x-2).
$$
Thus,
$$
y=x+1.
$$

To find the intersection with the line $$y=2x$$, set the two expressions for $$y$$ equal:
$$
x+1=2x.
$$
Solving for $$x$$:
$$
1=x,
$$
and substituting back into either equation, say $$y=2x$$:
$$
y=2(1)=2.
$$
Thus, the lines intersect at  
$$
(1,2).
$$
**(a) The gradient of line $$AB$$ is 1.** **(b) Draw the line $$y=2x$$ with a gradient of 2 and passing through the origin.** **(c) The two lines intersect at the point $$(1,2)$$.

(a) Find the gradient of the line .
(b) On the graph, draw the line with equation .
© Write down the coordinates of the point where the two lines intersect.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Geometry Questions

(a) Find the gradient of the line . (b) On the graph, draw the line with equation . © Write down the coordinates of the point where the two lines intersect.