Determine the equation of the following lines

Mathematics

2 answers:

Phantasy [73]3 years ago

7 0

Y=3x-1

y=4/3x+2

y=2/5x+5

SOVA2 [1]3 years ago

4 0

Hint: When an equation is parallel to another, they have the same slope and when it's perpendicular, the slope is inverted.

Let's start with the first one. Since it's parallel, we're keeping the slope which is 3. Now, you just plug in the coordinate pair and solve for the y-intercept.

4 = 3(1) + b
4 = 3 + b
b = 1

Therefore the equation would be y = 3x + 1.

Next one is perpendicular so we invert the slope to give it a negative-reciprocal, making the slope 4/3. Now, you plug in and solve.

-6 = 4/3(-3) + b
-6 = -8 + b
b = 2

Therefore, the equation is y = 4/3x + 2

Next, you need to put the equations into y=mx+b

Equation for slope:
5x + 2y -4 = 0
2y = -5x + 4
y = -5/2x + 2

Since the slope is perpendicular the slope would be 2/5.

Equation for y-intercept:
2x + 3y - 15 = 0
3y = -2x + 15
y = -2/3x + 5

Since it has the same y-intercept, it stays as a 5.

The final equation would be y = 2/5x + 5.

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Write an equation of the line in slope-intercept form. JY 1 (3, 3) (0, 2) 2 4 y=

stellarik [79]

Correct answer: y = $\frac{1}{3}$ x + 2

To find out the slope, you would need to remember this slope formula: $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ . We can use the two points provided on the graph to figure out the slope. We can label (3, 3) as $x_{1}$ and $y_{1}$ , and (0, 2) as $x_{2}$ and $y_{2}$ . Now we can plug these numbers into the slope formula to find out the slope:

m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ → $\frac{2-3}{0-3}$ → $\frac{-1}{-3}$ → $\frac{1}{3}$

To find out the y-intercept, just substitute (3, 3) into the slope-intercept formula ( y = mx + b ) with the slope that is substituted for 'm' that we already solved earlier.

y = mx + b

(3) = $\frac{1}{3}$ (3) + b

3 = 1 + b

2 = b

You can also prove this true by looking at the graph provided. The line intersects at the y-axis at 2.

Now we know that m = $\frac{1}{3}$ and b = 2, we can substitute it into the slope-intercept formula. Thus, the answer is y = $\frac{1}{3}$ x + 2.

Hope this helps you! Let me know if you have any more questions related to this problem.

3 0

3 years ago

Use the number line to add the fractions. help plz look at picture

mr_godi [17]

Answer: