Linear equations Show your work Solve for x x-4/y+2 = 5
1 answer:
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Answer:
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form:
where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)
- Parallel lines will always have the same slope but different y-intercepts.
<u>1) Determine the slope of the parallel line</u>
Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.
Switch the sides
Divide both sides by 2 to isolate y
Now that this equation is in slope-intercept form, we can easily identify that is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope
. Plug this into
:
<u>2) Determine the y-intercept</u>
Plug in the given point, (4,0)
Subtract both sides by 6
Therefore, -6 is the y-intercept of the line. Plug this into as b:
I hope this helps!
Answer:
See Below.
Step-by-step explanation:
We want to verify the equation:
To start, we can multiply the fraction by (1 - sin(θ)). This yields:
Simplify. The denominator uses the difference of two squares pattern:
Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:
Split into two separate fractions:
Rewrite the two fractions:
By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:
Hence verified.