2.1 Basic functions (linear)

Let [math]f(x)=ax+b[/math] be a linear function where [math]a[/math] and [math]b[/math] are real numbers. Suppose the [math]x[/math]-intercept of [math]f(x)[/math] is [math]-3[/math] and the [math]y[/math]-intercept of [math]f(x)[/math] is [math]-2[/math]. Find the value of [math]a[/math]. (fraction)

Let [math]\ell: y=m(x-a)[/math] be a line on the [math]xy[/math]-plane with negative slope where [math]a[/math] and [math]m[/math] are constants. If the angle between [math]\ell[/math] and the [math]x[/math]-axis is [math]45^\circ[/math] and [math]\ell[/math] passes though [math](3,0)[/math], what is the value of [math]am[/math]?

If [math]f(x)=2024(x-2025)+2026[/math], what is the value of [math]\dfrac{f(1026)-f(1024)}{2}[/math]?

The figure shows the graphs of [math]f(x)=ax+b, g(x)=cx+d[/math], and [math]h(x)=ex+f[/math] where [math]a, b, c, d, e, f[/math] are real numbers. Which statement is true?

The figure below shows the graph of [math]f(x)[/math].

(a) How many possible integers [math]n[/math] such that [math]f(n)[/math] is negative?

(b) The summation of the [math]x[/math]-intercepts and the [math]y[/math]-intercept of [math]f(x)[/math] is \underline{ (positive/negative/zero) }

(c) Let [math]m[/math] be a positive number. If [math]g(x)=mx-1[/math] and [math]f(x)[/math] have three intersections, then the range of [math]m[/math] is [math]a<m<b[/math] where [math]a[/math] and [math]b[/math] are constants, what is the value of [math]ab[/math]?

The area enclosed by [math]x+y=5, y=2x-4[/math] and [math]y[/math]-axis is?

A line equation is [math]7x+3y+4=0[/math], another line equation is [math]ax+by+m=0[/math], if two lines are perpendicular, and [math]a[/math] and [math]b[/math] are integer, what is leasts of [math]|a+b|[/math]?

If [math]f[/math] is a linear function such that [math]f(-1)=2.5[/math] and [math]f(1)=-3[/math], what is the value of [math]f(4)[/math]?

Using data collected from several donut shops, a linear regression was used to generate a model relating the price of a dozen donuts, [math]p[/math], in dollars, and the quantity sold, [math]d[/math], in dozens of donuts. The resulting equation was [math]d=-26.97p+342.80[/math]. What is the meaning of [math]-26.97[/math] in this model?

Which of the following is an equation of the line that contains the origin and is parallel to the line [math]2x-y=1[/math]?