Final answer:
To find the slope of the given equation, rearrange it and compare it to the standard form. For the line passing through the given point with the given slope, use the point-slope form of the equation. Rearrange the equation in slope-intercept form to find the slope.
Step-by-step explanation:
To find the slope of the line represented by the equation x²-x-2=-3x²+5x-52, we can rewrite the equation in the form y=mx+b, where m is the slope. Rearranging the equation gives us 4x²-6x-50=0. By comparing this equation to the standard form, we can see that the slope, m, is equal to -6.
For the line that passes through the points (3,4) and has a slope m=4, we can use the point-slope form of the equation, which is y-y₁=m(x-x₁). Plugging in the values, we get y-4=4(x-3). Simplifying gives us y=4x-8, which is the equation of the line passing through the given point with the given slope.
For the equation x-y=10, we can rearrange it to the slope-intercept form y=mx+b, where m is the slope. Doing so gives us y=x-10, so the slope of this line is 1.