Hi, I have to produce a sketch of a line that passes through the points (4,3) and (10,0), i have already worked its gradient out to be -0.5 and its y - intercepts as 5. For some reason i am having a mental block on the next bit! I need to add the line y = 6 to the sketch and then use algebra to find the coordinates of the point where the two lines intersect.

Question

Hi, I have to produce a sketch of a line that passes through the points (4,3) and (10,0), i have already worked its gradient out to be -0.5 and its y - intercepts as 5. For some reason i am having a mental block on the next bit! I need to add the line y = 6 to the sketch and then use algebra to find the coordinates of the point where the two lines intersect.

Please help

Answer 1

GIVEN: ( 4, 3 ), ( 10, 0 ).

m = -3/6 = -1/2 = -0.5
Find Equation of line:
Y = mX + b
3 = -1/2(4) + b.
Solve for b: b = 5.
Y = -1/2X +5
Substitute 6 for Y and solve for X.
6 = -1/2X + 5
1/2X = -1, X = -2. P ( -2, 6 ) is
where the lines intersect. Y = 6 is
a horizontal line 6 units above x
axis. Graph both lines and compare
point of intersection ( solution )
with calculated value.

Answer 2

Of course, I'll be happy to help you with that!

To start, let's sketch the line that passes through the points (4,3) and (10,0). We already know its gradient is -0.5 and its y-intercept is 5, so we have the equation of the line in slope-intercept form: y = -0.5x + 5.

Next, we need to add the line y = 6 to the sketch. This is a horizontal line that intersects the y-axis at 6. Since it is a horizontal line, its gradient is 0, and the equation remains y = 6.

Now, to find the point of intersection between the two lines using algebra, we can set their equations equal to each other. So we have:
-0.5x + 5 = 6

To solve this equation, subtract 5 from both sides:
-0.5x = 1

Then, we isolate x by dividing both sides by -0.5:
x = -2

Now, substitute this x-value back into either of the original equations to find the y-coordinate. Let's use the equation of the first line:
y = -0.5(-2) + 5
y = 1 + 5
y = 6

Therefore, the point of intersection for these two lines is (-2, 6).

So, to summarize:
1. Sketch the line y = -0.5x + 5 that passes through the points (4,3) and (10,0).
2. Add the line y = 6 to the sketch as a horizontal line passing through y = 6.
3. Set the two equations equal to each other: -0.5x + 5 = 6.
4. Solve for x: x = -2.
5. Substitute the x-value back into either equation to find the y-coordinate: y = 6.

I hope this helps! Let me know if you have any other questions.